How to animate proportional editing effect?
You could set up a grid, instance your cubes on its vertices, and then deform the grid using a Hook modifier...
The hook:

.. here, to an Empty. (Assignment of hooked vertices has to be done in Edit mode.)
This lets you keyframe the position of the hook, and the radius and strength of its influence. Much like Proportional Editing.
Here, one of the faces has been copied from the undistorted grid, and P separated to a new object. That has been parented to the grid, and instanced on each of its vertices by setting 'Vertices' in the grid's Object Properties tab &gt; Instancing panel.